Let (2 , ) be the largest interval in which the function f(t)= |t+1| t^ 2 , t 2, is \_\_\_\_

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Correct answer: A. A

For t For -1 f(t) = t+1 t^2 , so f'(t) = -(t+2) t^3 > 0 (increasing). For t f(t) = -t-1 t^2 , so f'(t) = t+2 t^3 . For -2 f'(t) For t f'(t) > 0 (increasing). Largest decreasing interval is (-2, -1) = (2 , ), so = -1. For g(x) = 2 (x-2) - x^2 + 4x + 1: g'(x) = 2 x-2 - 2x + 4 = 0 gives (x-2)^2 = 1, so x = 3. Since g''(x) = - 2 (x-2)^2 - 2 g(3) = 2 (1) - 9 + 12 + 1 = 4

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